What verb represents acting with optimism, enthusiasm and vitality?
As in an admonition, "Go forth and ______." "A leader must be seen to _______." Perhaps it is a word similar to vivify, vitalize, strive, thrive, prosper or inspire.
Try rally. The full text at the last link captures more of the optimism, enthusiasm and vitality you mention in your question.
2a : to arouse for action - M-W
1 (Of troops) come together again in order to continue fighting after a defeat or dispersion: 'De Montfort’s troops rallied and drove back the king’s infantry' - oxforddictionaries.com
When you hit that last mile in the race and are so tired you want to quit, that's when you rally, finding the strength to pick up the pace. - vocabulary.com
It's somewhat difficult to find a good antonym verb for procrastinate. Go forth and procrastinate!
First thing that came to mind is the traditional idiom carpe diem or seize the day. "Seize" is at least a verb and can be imperative.
A good adjective is proactive.
But for verbs, I first thought execute as fitting as long as it's clear by context which meaning you are using. Since both your examples are intransitive, perhaps it is clear:
execute - intransitive verb:
to perform properly or skillfully the fundamentals of a sport ...
To execute means to carry out in full or perform. If you execute all the difficult steps of the dance perfectly, you will make your instructor proud.
Accomplish is also a close synonym, though I see it as less imperative than execute.
Go forth and conquer.
A leader must be seen to conquer adversity.
Though there are moral implications to conquest, one has to be optimistic, enthusiastic and energetic to be a conqueror. I would expect the surrounding text to provide context as to whether the negative moral implications of conquest apply to this person, or whether inspirational leadership in overcoming all obstacles is intended.